Electronic Journal of Differential Equations, Vol. 2010(2010), No. 75, pp. 1-15. Title: Reaction-diffusion system of equations in non-stationary medium and arbitrary non-smooth domains Author: Sikiru Adigun Sanni (Univ. of Uyo, Nigeria) Submitted November 27, 2009. Published May 21, 2010. Math Subject Classifications: 35B40, 35K57, 80A25. Key Words: Irreversible reaction; reactant diffusivity; thermal conductivity; a priori estimates; Banach's fixed point theorem.